131 lines
3.9 KiB
TeX
Executable File
131 lines
3.9 KiB
TeX
Executable File
\documentclass[
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solutions,
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hidewarning,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\title{Warm-Up: Conway's Box}
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\subtitle{Prepared by \githref{Mark} on \today. \\ Based on a true story.}
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\usetikzlibrary{shapes}
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\tikzset{
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iso/.style={kite, draw, kite vertex angles=120, minimum size=1cm, outer sep=0pt}
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}
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\newcommand{\isogrid}[2]{
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\foreach \i [count=\row from 0, remember=\row as \lastrow (initially 0)] in {0,...,#1}{
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\foreach \j [count=\col from 0, remember=\col as \lastcol (initially 0)] in {0,...,#2}{
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\ifnum\row=0
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\ifnum\col=0
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\node[iso] (\row-\col) {};
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\else
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\node[iso, anchor=left vertex] (\row-\col) at (\row-\lastcol.right vertex) {};
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\fi
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\else
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\ifnum\col=0
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\node[iso, anchor=upper vertex] (\row-\col) at (\lastrow-\col.lower vertex) {};
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\else
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\node[iso, anchor=left vertex] (\row-\col) at (\row-\lastcol.right vertex) {};
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\fi
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\fi
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}
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}
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\draw (0-0.left vertex)--(#1-0.left vertex);
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\foreach \i in {0,...,#2}{
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\draw (0-\i.upper vertex)--(#1-\i.lower vertex);
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\draw (0-\i.right vertex)--(#1-\i.right vertex);
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}
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}
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\begin{document}
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\maketitle
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\problem{}
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Pack the following pieces into a $5\times5\times5$ box.\par
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\begin{itemize}
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\item One $2 \times 2 \times 2$
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\item Two $1 \times 2 \times 2$
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\item Three $1 \times 1 \times 3$
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\item Thirteen $1 \times 2 \times 4$
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\end{itemize}
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\begin{solution}
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\begin{center}
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\includegraphics[width=10cm,page=1]{conway_sol.pdf}
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\end{center}
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\end{solution}
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\vfill
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\pagebreak
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\begin{center}
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\null\vfill
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\begin{tikzpicture}
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\isogrid{20}{7}
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\end{tikzpicture}
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\vfill\null
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\end{center}
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\end{document}
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% \documentclass[tikz,border=2mm]{standalone}
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% \usetikzlibrary{shapes}
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%
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% \tikzset{
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% iso/.style={kite, draw, kite vertex angles=120, minimum size=1cm, outer sep=0pt}
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% }
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%
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% \newcommand{\isogrid}[2]{
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% \foreach \i [count=\row from 0, remember=\row as \lastrow (initially 0)] in {0,...,#1}{
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% \foreach \j [count=\col from 0, remember=\col as \lastcol (initially 0)] in {0,...,#2}{
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% \ifnum\row=0
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% \ifnum\col=0
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% \node[iso] (\row-\col) {\row-\col};
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% \else
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% \node[iso, anchor=left vertex] (\row-\col) at (\row-\lastcol.right vertex) {\row-\col};
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% \fi
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% \else
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% \ifnum\col=0
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% \node[iso, anchor=upper vertex] (\row-\col) at (\lastrow-\col.lower vertex) {\row-\col};
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% \else
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% \node[iso, anchor=left vertex] (\row-\col) at (\row-\lastcol.right vertex) {\row-\col};
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% \fi
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% \fi
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% }
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% }
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% \draw (0-0.left vertex)--(#1-0.left vertex);
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% \foreach \i in {0,...,#2}{
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% \draw (0-\i.upper vertex)--(#1-\i.lower vertex);
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% \draw (0-\i.right vertex)--(#1-\i.right vertex);
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% }
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% }
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%
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% \begin{document}
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% \begin{tikzpicture}
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%
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% \isogrid{19}{9}
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% \begin{scope}[line width=2pt]
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% \draw (1-3.right vertex)--(3-5.right vertex)--(7-1.right vertex)--(5-0.left vertex)--cycle;
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% \draw (5-0.left vertex)--(13-0.left vertex)--(15-1.right vertex)--(7-1.right vertex);
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% \draw (3-5.right vertex)--(5-5.right vertex)--(7-7.right vertex)--(10-7.right vertex)--(11-8.right vertex)--(12-7.right vertex)--(13-8.right vertex)--(15-7.upper vertex)--(13-5.upper vertex)--(10-5.upper vertex)--(8-3.upper vertex)--(5-5.right vertex);
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% \draw (9-5.lower vertex)--(7-7.right vertex);
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% \draw (12-5.lower vertex)--(10-7.right vertex);
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% \draw (11-8.right vertex)--(16-8.right vertex)--(17-7.lower vertex)--(13-3.lower vertex)--(15-1.right vertex);
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% \draw (7-3.lower vertex)--(13-3.lower vertex);
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% \draw (14-7.lower vertex)--(17-7.lower vertex);
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%
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% \draw[dashed] (13-0.left vertex)--(9-3.right vertex)--(1-3.right vertex);
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% \draw[dashed] (9-3.right vertex)--(14-8.right vertex)--(15-7.right vertex)--(16-8.right vertex);
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% \draw[dashed] (12-7.right vertex)--(15-7.right vertex);
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% \end{scope}
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% \end{tikzpicture}
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%
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% \end{document} |